Problem

Let $\lim _{x \rightarrow 2} f(x)=36$. Use the limit rules to find the following limit.
\[
\lim _{x \rightarrow 2} \sqrt{f(x)}
\]
\[
\lim _{x \rightarrow 2} \sqrt{f(x)}=
\]

Answer

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Answer

Final Answer: The limit as x approaches 2 of the square root of f(x) is \(\boxed{6}\)

Steps

Step 1 :Given that \(\lim _{x \rightarrow 2} f(x)=36\)

Step 2 :Use the limit rules to find the following limit: \(\lim _{x \rightarrow 2} \sqrt{f(x)}\)

Step 3 :The limit of a function as x approaches a certain value is the value that the function approaches as x gets closer and closer to that value. In this case, we are given that as x approaches 2, f(x) approaches 36.

Step 4 :We are asked to find the limit as x approaches 2 of the square root of f(x). Since we know that the limit as x approaches 2 of f(x) is 36, we can substitute 36 in place of f(x) in the expression we are asked to find the limit of. This gives us the square root of 36.

Step 5 :The square root of 36 is 6, so the limit as x approaches 2 of the square root of f(x) is 6.

Step 6 :Final Answer: The limit as x approaches 2 of the square root of f(x) is \(\boxed{6}\)

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